The League One club are looking for a new manager after parting company with Paul Groves and his assistant Shaun Brooks on Wednesday.
It came less than 24 hours after the 3-1 defeat to Crawley which sent the Cherries fifth from bottom, with just one win from 10 League games.
Former Tottenham boss Redknapp recently returned to the south-coast club - where he began his career in management in 1983 - in an advisory role.
Redknapp and former manager Eddie Howe, now at Burnley, are among the early favourites for the job.
But when asked whether Redknapp could take caretaker charge for Saturday's trip to Coventry, Mitchell told Hot Radio: "We've spoken about the football club and the best way forward and Harry knows my feelings but I can't say much more than that.
"Harry is his own man and he's got the capability to manage at a club much higher than a League One club, but that's where we are at the moment."